The Graph Augmented Multi-layer Perceptron (GA-MLP) model is an attractive alternative to Graph Neural Networks (GNNs). This is because it is resistant to the over-smoothing problem, and deeper GA-MLP models yield better performance. GA-MLP models are traditionally optimized by the Stochastic Gradient Descent (SGD). However, SGD suffers from the layer dependency problem, which prevents the gradients of different layers of GA-MLP models from being calculated in parallel. In this paper, we propose a parallel deep learning Alternating Direction Method of Multipliers (pdADMM) framework to achieve model parallelism: parameters in each layer of GA-MLP models can be updated in parallel. The extended pdADMM-Q algorithm reduces communication cost by utilizing the quantization technique. Theoretical convergence to a critical point of the pdADMM algorithm and the pdADMM-Q algorithm is provided with a sublinear convergence rate $o(1/k)$. Extensive experiments in six benchmark datasets demonstrate that the pdADMM can lead to high speedup, and outperforms all the existing state-of-the-art comparison methods.
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